# Need help finding Diagonals of a Rhombus

• MHB
• thatbluegsx90
In summary, the person is trying to make a terrarium and needs to find the diagonal measurements of the top cover. Using the information provided, it can be determined that the distance "A" is approximately 11 inches and the distance "B" is approximately 8.485 inches. The sides of the rhombus are approximately 7.2 inches and the angles at $A_1$ and $A_2$ are almost exactly 72 degrees.
thatbluegsx90
Not sure where exactly to post this but I think it fits in this category...I recently got interested in making a Terrarium and plan to make the glass enclosure myself.. for the life of me without having the physical thing in front of me I can't figure out one of the diagonal measurements of the top cover.. I apologize for the rough drawing but I'm looking for what A and B are(didn't mean to put the X in there)... I'm about 60% confident that B is 8 1/2 but I has been a while since I've done anything related to this

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From your middle, side view, the back height of the terrarium is 16", the front is 8", and the base is 6". If you draw a line from the top of the front perpendicular to the back (so parallel to the base) you have a right triangle with height 16- 8= 8" and base 8". By the Pythagorean theorem, your distance "A" satisfies $$A^2= 8^2+ 8^2= 64+ 64= 120$$. So $$A= \sqrt{120}= 2\sqrt{15}$$ or about 11" (10.954...). Your distance "B" is just the distance across which is 6+ 6= 12".

thatbluegsx90 said:
Not sure where exactly to post this but I think it fits in this category...I recently got interested in making a Terrarium and plan to make the glass enclosure myself.. for the life of me without having the physical thing in front of me I can't figure out one of the diagonal measurements of the top cover.. I apologize for the rough drawing but I'm looking for what A and B are(didn't mean to put the X in there)... I'm about 60% confident that B is 8 1/2 but I has been a while since I've done anything related to this
[TIKZ][scale=0.5]
\coordinate (A) at (-5,2) ;
\coordinate (B) at (1,3) ;
\coordinate (C) at (6,1) ;
\coordinate (D) at (0,0) ;
\coordinate [label=left: $B_1$] (E) at (-5,14) ;
\coordinate [label=above right: $A_1$] (F) at (1,19) ;
\coordinate [label=right: $B_2$] (G) at (6,13) ;
\coordinate [label=left: $A_2$] (H) at (0,8) ;
\draw [very thick] (G) --node
{$12$} (C) --node[below] {$6$} (D) --node[below] {$6$} (A) --node
{$12$} (E) -- (H) ;
\draw [very thick] (E) -- (F) -- (G) -- (H) --node
{$8$} (D) ;
\draw [dashed] (A) -- (B) -- (C) ;
\draw [dashed] (B) --node
{$16$} (F) ;
[/TIKZ]​

In my picture, the distance between $A_1$ and $A_2$ is your distance $A$, and the distance between $B_1$ and $B_2$ is your distance $B$.

Both of the points $B_1$, $B_2$ are $12$ inches above diagonally opposite points of the base of the terrarium. So the distance between them is $6\sqrt2$, which is approximately $8.485$ (close to your estimate of 8 1/2, but a bit less).

The horizontal distance between $A_1$ and $A_2$ is again $6\sqrt2$, but there is also a vertical separation of $16 - 8 = 8$ between them. It follows from Pythagoras's theorem that $A = \sqrt{72 + 64} = \sqrt{136}$, which is approximately $11.66$.

If it helps you in cutting the glass, the sides of the rhombus are approximately $7.2$ inches. The angles at $A_1$ and $A_2$ are almost exactly $72^\circ$ (and the angles at $B_1$ and $B_2$ are almost exactly $108^\circ$).​

## 1. What is a rhombus?

A rhombus is a quadrilateral (a shape with four sides) with four equal sides. It is also known as a diamond or a lozenge.

## 2. How do you find the diagonals of a rhombus?

To find the diagonals of a rhombus, you can use the formula d1 = √(a^2 + b^2) and d2 = √(a^2 + b^2), where a and b are the lengths of the sides of the rhombus.

## 3. Are the diagonals of a rhombus equal?

Yes, the diagonals of a rhombus are always equal in length. This is because a rhombus is a special type of parallelogram, and the diagonals of parallelograms bisect each other.

## 4. Can you find the diagonals of a rhombus using only the length of one side?

Yes, you can find the diagonals of a rhombus using only the length of one side. Since all four sides of a rhombus are equal, you can use the formula d = s√2, where d is the length of the diagonal and s is the length of one side.

## 5. How are the diagonals of a rhombus related to its angles?

The diagonals of a rhombus bisect each other at right angles. This means that the angles formed by the diagonals and the sides of the rhombus are all right angles.

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